The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
We show that solutions of the 2D Fokker-Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf-Cole transformation relates the 2D equatio...
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Elsevier Ltd
2016
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| 003 | AR-BaUEN | ||
| 005 | 20230518205621.0 | ||
| 008 | 190411s2016 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84940068507 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a NOAND | ||
| 100 | 1 | |a Cañizo, J.A. | |
| 245 | 1 | 4 | |a The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| 260 | |b Elsevier Ltd |c 2016 | ||
| 270 | 1 | 0 | |m Carrillo, J.A.; Department of Mathematics, Imperial College London, South Kensington CampusUnited Kingdom; email: carrillo@imperial.ac.uk |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a We show that solutions of the 2D Fokker-Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf-Cole transformation relates the 2D equation in radial coordinates to the usual linear Fokker-Planck equation. Hence, radially symmetric solutions can be computed analytically, and our results for general (non radially symmetric) solutions follow from comparison and entropy arguments. In order to show convergence to equilibrium we also prove a version of the Csiszár-Kullback inequality for the Bose-Einstein-Fokker-Planck entropy functional. © 2015 Elsevier Ltd. All rights reserved. |l eng | |
| 536 | |a Detalles de la financiación: Engineering and Physical Sciences Research Council, EPSRC, EP/K008404/1 | ||
| 536 | |a Detalles de la financiación: MTM2011-27739-C04-02 | ||
| 536 | |a Detalles de la financiación: Wolfson College, University of Oxford | ||
| 536 | |a Detalles de la financiación: KineticCF | ||
| 536 | |a Detalles de la financiación: MTM2014-52056-P | ||
| 536 | |a Detalles de la financiación: Royal Society | ||
| 536 | |a Detalles de la financiación: The authors would like to warmly thank the anonymous referee for useful comments. The authors acknowledge support from the Spanish project MTM2011-27739-C04-02. J. A. Cañizo acknowledges support from the Marie-Curie CIG project KineticCF and the Spanish project MTM2014-52056-P. J. A. Carrillo acknowledges support from the Royal Society through a Wolfson Research Merit Award and the Engineering and Physical Sciences Research Council (UK) grant number EP/K008404/1 . | ||
| 593 | |a Departamento de Matemática Aplicada, Universidad de Granada, Granada, 18071, Spain | ||
| 593 | |a Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom | ||
| 593 | |a Institut de Mathématiques de Toulouse, UMRA 5219, Université de Toulouse, CNRS, Toulouse Cedex 9, F-31062, France | ||
| 593 | |a Departamento de Matemática, Universidad de Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a BOSE-EINSTEIN |
| 690 | 1 | 0 | |a ENTROPY METHOD |
| 690 | 1 | 0 | |a LONG-TIME ASYMPTOTICS |
| 690 | 1 | 0 | |a BOSONS |
| 690 | 1 | 0 | |a LINEAR TRANSFORMATIONS |
| 690 | 1 | 0 | |a MATHEMATICAL TRANSFORMATIONS |
| 690 | 1 | 0 | |a STATISTICAL MECHANICS |
| 690 | 1 | 0 | |a TIMING JITTER |
| 690 | 1 | 0 | |a ASYMPTOTIC BEHAVIORS |
| 690 | 1 | 0 | |a BOSE-EINSTEIN |
| 690 | 1 | 0 | |a CONVERGENCE TO EQUILIBRIUM |
| 690 | 1 | 0 | |a ENTROPY FUNCTIONAL |
| 690 | 1 | 0 | |a ENTROPY METHODS |
| 690 | 1 | 0 | |a HOPF-COLE TRANSFORMATIONS |
| 690 | 1 | 0 | |a LONG-TIME ASYMPTOTICS |
| 690 | 1 | 0 | |a RADIALLY SYMMETRIC SOLUTION |
| 690 | 1 | 0 | |a FOKKER PLANCK EQUATION |
| 700 | 1 | |a Carrillo, J.A. | |
| 700 | 1 | |a Laurençot, P. | |
| 700 | 1 | |a Rosado, J. | |
| 773 | 0 | |d Elsevier Ltd, 2016 |g v. 137 |h pp. 291-305 |p Nonlinear Anal Theory Methods Appl |x 0362546X |w (AR-BaUEN)CENRE-254 |t Nonlinear Analysis, Theory, Methods and Applications | |
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